Contents

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very fake, etc.... As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very quite.

In mathematics, logic, linguistics, and other abstract disciplines, the systems are not assigned to objects. They are defined by an enumeration of the variables, their admissible values, and their algebraic, topological, grammatical, and other properties which, in the given case, determine the relations between the variables under consideration.

p. 40.

No classification is complete and perfect for all purposes.

p. 69.

Applying this approach, systems belonging to different scientific disciplines are investigated in their natural forms. On the basis of experimental results, isomorphic relations between different systems are studied and, finally, some general principles applicable for all systems of a certain class are formulated.

Among the various paradigmatic changes in science and mathematics in this century, one such change concerns the concept of uncertainty. In science, this change has been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it. According to the traditional view, science should strive for certainty in all its manifestations (precision, specificity, sharpness, consistency, etc.); hence, uncertainty (imprecision, nonspecificity, vagueness, inconsistency,etc.) is regarded as unscientific. According to the alternative (or modem) view, uncertainty is considered essential to science; it is not only an unavoidable plague, but it has, in fact, a great utility.

p. 1.

The first stage of the transition from the traditional view to the modem view of uncertainty began in the late 19th century, when physics became concerned with processes at the molecular level.

p. 1.

The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.

p. 1-2.

The emergence of computer technology in World War II and its rapidly growing power in the second half of this century made it possible to deal with increasingly complex problems, some of which began to resemble the notion of organized complexity. Initially, it was the common belief of many scientists that the level of complexity we can handle is basically a matter of the level of computational power at our disposal. Later, in the early 1960s, this naive belief was replaced with a more realistic outlook.

p. 2.

In spite of the insurmountable computational limits, we continue to pursue the many problems that possess the characteristics of organized complexity. These problems are too important for our well being to give up on them. The main challenge in pursuing these problems narrows down fundamentally to one question: how to deal with systems and associated problems whose complexities are beyond our information processing limits? That is, how can we deal with these problems if no computational power alone is sufficient?

p. 2-3.

Probability theory is an ideal tool for formalizing uncertainty in situations where class frequencies are known or where evidence is based on outcomes of a sufficiently long series of independent random experiments. Possibility theory, on the other hand, is ideal for formalizing incomplete information expressed in terms of fuzzy propositions.

To select an appropriate fuzzy implication for approximate reasoning under each particular situation is a difficult problem. Although some theoretically supported guidelines are now available for some situations, we are still far from a general solution to this problem.

What is systems science? This question, which I have been asked on countless occasions, can basically be answered either in terms of activities associated with systems science or in terms of the domain of its inquiry. The most natural answers to the question are, almost inevitably, the following deﬁnitions:

Systems science is what systems scientists do when they claim they do science.

Systems science is that field of scientific inquiry whose objects of study are systems.

Without further explanation, these deﬁnitions are clearly of little use.

p. 3.

The term “system” is unquestionably one of the most widely used terms not only in science, but in other areas of human endeavor as well. It is a highly overworked term, which enjoys different meanings under different circumstances and for different people. However, when separated from its specific connotations and uses, the term "system" is almost never explicitly defined.